The answer is maybe.
When your credit utilization rate is high card issuers sometimes lower your limit or cancel your card as you pay down the limit. Thus, as you pay down your limit you could face a chain of closed accounts. This won't be effected by the balance transfer, it is merely a side effect of using a lot of your available credit.
The fact that you transfer a balance itself won't hurt your credit. The new credit line you opened will hurt your credit (temporarily...though probably good in the long run). The new hard inquiry to get the account will hurt your credit. The reduced average age of all your accounts will hurt your credit. The reduced debt utilization percentage due to your new available credit will help your credit. The balance transfer in itself won't hurt your credit.
Note: A balance transfer might temporarily lower your credit score. If you have card A with a 1000 dollar balance and card B with 0% APR and no balance and you transfer the 1000 dollars to card B, your credit report might temporarily show you running a 1000 dollar balance on both card A and B since it takes a few weeks for the transfer to fully go through sometimes. Also, most issuers only report to credit bureaus once a month. So depending on the timing of the reports you might have a report that shows a 2000 dollar balance for a month under the hypothetical facts I mentioned. This would temporarily hurt your credit score.
